nLab finitely presentable group (Rev #4)

Finitely presented groups

Idea

A group $G$ is finitely presentable if it has a finite presentation, i.e., there is a group presentation, $\langle X: R\rangle$ , for $G$ with both its set, $X$ , of generators and its set, $R$ , of relations being finite sets.

Remark

The term ‘finitely presented’ is often used rather than `finitely presentable', however 'finitely presented' would seem to imply that a given finite presentation was intended, whilst here only the existence of one is required.

Related concepts

finitely generated group

References

Useful elementary or introductory texts, include

D. L. Johnson, Presentations of Groups (London Mathematical Society Student Texts 15) 1990, Cambridge Univ. Press,

and the earlier:

D. L. Johnson, Topics in Theory of Group Presentations, London Mathematical Society Lecture notes series 42) 1980, Cambridge Univ. Press.

Revision on January 17, 2023 at 17:13:28 by Urs Schreiber See the history of this page for a list of all contributions to it.